Observation of Z
cð3900Þ
0in e
þe
−→ π
0π
0J=ψ
M. Ablikim,1M. N. Achasov,9,f X. C. Ai,1 O. Albayrak,5 M. Albrecht,4 D. J. Ambrose,44A. Amoroso,48a,48c F. F. An,1 Q. An,45,a J. Z. Bai,1 R. Baldini Ferroli,20a Y. Ban,31D. W. Bennett,19 J. V. Bennett,5 M. Bertani,20aD. Bettoni,21a J. M. Bian,43F. Bianchi,48a,48cE. Boger,23,dI. Boyko,23R. A. Briere,5H. Cai,50X. Cai,1,aO. Cakir,40a,bA. Calcaterra,20a G. F. Cao,1S. A. Cetin,40bJ. F. Chang,1,aG. Chelkov,23,d,eG. Chen,1H. S. Chen,1H. Y. Chen,2J. C. Chen,1M. L. Chen,1,a S. J. Chen,29X. Chen,1,aX. R. Chen,26Y. B. Chen,1,a H. P. Cheng,17X. K. Chu,31G. Cibinetto,21aH. L. Dai,1,aJ. P. Dai,34 A. Dbeyssi,14D. Dedovich,23Z. Y. Deng,1A. Denig,22I. Denysenko,23M. Destefanis,48a,48cF. De Mori,48a,48cY. Ding,27 C. Dong,30J. Dong,1,aL. Y. Dong,1M. Y. Dong,1,aS. X. Du,52P. F. Duan,1E. E. Eren,40bJ. Z. Fan,39J. Fang,1,aS. S. Fang,1 X. Fang,45,aY. Fang,1L. Fava,48b,48cF. Feldbauer,22G. Felici,20aC. Q. Feng,45,aE. Fioravanti,21aM. Fritsch,14,22C. D. Fu,1
Q. Gao,1 X. Y. Gao,2Y. Gao,39Z. Gao,45,a I. Garzia,21a C. Geng,45,aK. Goetzen,10W. X. Gong,1,a W. Gradl,22 M. Greco,48a,48cM. H. Gu,1,a Y. T. Gu,12Y. H. Guan,1A. Q. Guo,1 L. B. Guo,28Y. Guo,1Y. P. Guo,22Z. Haddadi,25 A. Hafner,22S. Han,50Y. L. Han,1X. Q. Hao,15F. A. Harris,42K. L. He,1Z. Y. He,30T. Held,4Y. K. Heng,1,aZ. L. Hou,1
C. Hu,28H. M. Hu,1 J. F. Hu,48a,48c T. Hu,1,a Y. Hu,1 G. M. Huang,6G. S. Huang,45,a H. P. Huang,50J. S. Huang,15 X. T. Huang,33Y. Huang,29T. Hussain,47Q. Ji,1Q. P. Ji,30X. B. Ji,1X. L. Ji,1,a L. L. Jiang,1L. W. Jiang,50X. S. Jiang,1,a X. Y. Jiang,30J. B. Jiao,33Z. Jiao,17D. P. Jin,1,aS. Jin,1T. Johansson,49A. Julin,43N. Kalantar-Nayestanaki,25X. L. Kang,1 X. S. Kang,30M. Kavatsyuk,25B. C. Ke,5 P. Kiese,22R. Kliemt,14B. Kloss,22O. B. Kolcu,40b,iB. Kopf,4M. Kornicer,42 W. Kühn,24A. Kupsc,49J. S. Lange,24M. Lara,19P. Larin,14C. Leng,48cC. Li,49C. H. Li,1Cheng Li,45,aD. M. Li,52F. Li,1,a G. Li,1H. B. Li,1J. C. Li,1Jin Li,32K. Li,33K. Li,13Lei Li,3P. R. Li,41T. Li,33W. D. Li,1W. G. Li,1X. L. Li,33X. M. Li,12 X. N. Li,1,aX. Q. Li,30Z. B. Li,38H. Liang,45,aY. F. Liang,36Y. T. Liang,24G. R. Liao,11D. X. Lin,14B. J. Liu,1C. X. Liu,1 F. H. Liu,35Fang Liu,1Feng Liu,6H. B. Liu,12H. H. Liu,16H. H. Liu,1H. M. Liu,1J. Liu,1J. B. Liu,45,aJ. P. Liu,50J. Y. Liu,1 K. Liu,39K. Y. Liu,27L. D. Liu,31P. L. Liu,1,a Q. Liu,41S. B. Liu,45,a X. Liu,26X. X. Liu,41Y. B. Liu,30Z. A. Liu,1,a Zhiqiang Liu,1Zhiqing Liu,22H. Loehner,25X. C. Lou,1,a,hH. J. Lu,17J. G. Lu,1,aR. Q. Lu,18Y. Lu,1Y. P. Lu,1,aC. L. Luo,28 M. X. Luo,51T. Luo,42X. L. Luo,1,aM. Lv,1X. R. Lyu,41F. C. Ma,27H. L. Ma,1L. L. Ma,33Q. M. Ma,1T. Ma,1X. N. Ma,30 X. Y. Ma,1,aF. E. Maas,14M. Maggiora,48a,48cY. J. Mao,31Z. P. Mao,1S. Marcello,48a,48cJ. G. Messchendorp,25J. Min,1,a T. J. Min,1R. E. Mitchell,19X. H. Mo,1,aY. J. Mo,6C. Morales Morales,14K. Moriya,19N. Yu. Muchnoi,9,fH. Muramatsu,43 Y. Nefedov,23F. Nerling,14I. B. Nikolaev,9,f Z. Ning,1,a S. Nisar,8 S. L. Niu,1,a X. Y. Niu,1 S. L. Olsen,32Q. Ouyang,1,a S. Pacetti,20bP. Patteri,20aM. Pelizaeus,4H. P. Peng,45,aK. Peters,10J. Pettersson,49J. L. Ping,28R. G. Ping,1R. Poling,43 V. Prasad,1Y. N. Pu,18M. Qi,29S. Qian,1,aC. F. Qiao,41L. Q. Qin,33N. Qin,50X. S. Qin,1Y. Qin,31Z. H. Qin,1,aJ. F. Qiu,1
K. H. Rashid,47C. F. Redmer,22H. L. Ren,18M. Ripka,22G. Rong,1 Ch. Rosner,14X. D. Ruan,12V. Santoro,21a A. Sarantsev,23,gM. Savrié,21bK. Schoenning,49S. Schumann,22W. Shan,31M. Shao,45,a C. P. Shen,2 P. X. Shen,30 X. Y. Shen,1H. Y. Sheng,1W. M. Song,1X. Y. Song,1S. Sosio,48a,48cS. Spataro,48a,48cG. X. Sun,1J. F. Sun,15S. S. Sun,1 Y. J. Sun,45,aY. Z. Sun,1 Z. J. Sun,1,a Z. T. Sun,19C. J. Tang,36X. Tang,1 I. Tapan,40c E. H. Thorndike,44M. Tiemens,25 M. Ullrich,24I. Uman,40bG. S. Varner,42B. Wang,30B. L. Wang,41D. Wang,31D. Y. Wang,31K. Wang,1,a L. L. Wang,1 L. S. Wang,1M. Wang,33P. Wang,1P. L. Wang,1 S. G. Wang,31W. Wang,1,aX. F. Wang,39Y. D. Wang,14Y. F. Wang,1,a Y. Q. Wang,22Z. Wang,1,aZ. G. Wang,1,aZ. H. Wang,45,aZ. Y. Wang,1T. Weber,22D. H. Wei,11J. B. Wei,31P. Weidenkaff,22 S. P. Wen,1 U. Wiedner,4 M. Wolke,49L. H. Wu,1Z. Wu,1,aL. G. Xia,39Y. Xia,18D. Xiao,1 Z. J. Xiao,28Y. G. Xie,1,a Q. L. Xiu,1,aG. F. Xu,1L. Xu,1Q. J. Xu,13Q. N. Xu,41X. P. Xu,37L. Yan,45,a W. B. Yan,45,aW. C. Yan,45,a Y. H. Yan,18 H. J. Yang,34H. X. Yang,1L. Yang,50Y. Yang,6Y. X. Yang,11H. Ye,1M. Ye,1,aM. H. Ye,7J. H. Yin,1B. X. Yu,1,aC. X. Yu,30
H. W. Yu,31J. S. Yu,26C. Z. Yuan,1 W. L. Yuan,29Y. Yuan,1 A. Yuncu,40b,c A. A. Zafar,47A. Zallo,20a Y. Zeng,18 B. X. Zhang,1 B. Y. Zhang,1,aC. Zhang,29C. C. Zhang,1 D. H. Zhang,1H. H. Zhang,38H. Y. Zhang,1,a J. J. Zhang,1 J. L. Zhang,1J. Q. Zhang,1J. W. Zhang,1,aJ. Y. Zhang,1J. Z. Zhang,1K. Zhang,1L. Zhang,1S. H. Zhang,1X. Y. Zhang,33 Y. Zhang,1Y. N. Zhang,41Y. H. Zhang,1,aY. T. Zhang,45,aYu Zhang,41Z. H. Zhang,6Z. P. Zhang,45Z. Y. Zhang,50G. Zhao,1 J. W. Zhao,1,a J. Y. Zhao,1 J. Z. Zhao,1,a Lei Zhao,45,a Ling Zhao,1 M. G. Zhao,30Q. Zhao,1 Q. W. Zhao,1 S. J. Zhao,52 T. C. Zhao,1Y. B. Zhao,1,aZ. G. Zhao,45,a A. Zhemchugov,23,d B. Zheng,46J. P. Zheng,1,a W. J. Zheng,33Y. H. Zheng,41 B. Zhong,28L. Zhou,1,aLi Zhou,30X. Zhou,50X. K. Zhou,45,aX. R. Zhou,45,aX. Y. Zhou,1K. Zhu,1K. J. Zhu,1,aS. Zhu,1
X. L. Zhu,39Y. C. Zhu,45,a Y. S. Zhu,1 Z. A. Zhu,1 J. Zhuang,1,a L. Zotti,48a,48c B. S. Zou,1 and J. H. Zou1 (BESIII Collaboration)
1Institute of High Energy Physics, Beijing 100049, People’s Republic of China 2
Beihang University, Beijing 100191, People’s Republic of China
3Beijing Institute of Petrochemical Technology, Beijing 102617, People’s Republic of China
4
Bochum Ruhr-University, D-44780 Bochum, Germany
5Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
6
Central China Normal University, Wuhan 430079, People’s Republic of China
7China Center of Advanced Science and Technology, Beijing 100190, People’s Republic of China
8
COMSATS Institute of Information Technology, Lahore, Defence Road, Off Raiwind Road, 54000 Lahore, Pakistan
9G.I. Budker Institute of Nuclear Physics SB RAS (BINP), Novosibirsk 630090, Russia
10
GSI Helmholtzcentre for Heavy Ion Research GmbH, D-64291 Darmstadt, Germany
11Guangxi Normal University, Guilin 541004, People’s Republic of China
12
GuangXi University, Nanning 530004, People’s Republic of China
13Hangzhou Normal University, Hangzhou 310036, People’s Republic of China
14
Helmholtz Institute Mainz, Johann-Joachim-Becher-Weg 45, D-55099 Mainz, Germany
15Henan Normal University, Xinxiang 453007, People’s Republic of China
16
Henan University of Science and Technology, Luoyang 471003, People’s Republic of China
17Huangshan College, Huangshan 245000, People’s Republic of China
18
Hunan University, Changsha 410082, People’s Republic of China
19Indiana University, Bloomington, Indiana 47405, USA
20a
INFN Laboratori Nazionali di Frascati, I-00044, Frascati, Italy
20bINFN and University of Perugia, I-06100, Perugia, Italy
21a
INFN Sezione di Ferrara, I-44122, Ferrara, Italy
21bUniversity of Ferrara, I-44122, Ferrara, Italy
22
Johannes Gutenberg University of Mainz, Johann-Joachim-Becher-Weg 45, D-55099 Mainz, Germany
23Joint Institute for Nuclear Research, 141980 Dubna, Moscow region, Russia
24
Justus Liebig University Giessen, II. Physikalisches Institut, Heinrich-Buff-Ring 16, D-35392 Giessen, Germany
25KVI-CART, University of Groningen, NL-9747 AA Groningen, Netherlands
26
Lanzhou University, Lanzhou 730000, People’s Republic of China
27Liaoning University, Shenyang 110036, People’s Republic of China
28
Nanjing Normal University, Nanjing 210023, People’s Republic of China
29Nanjing University, Nanjing 210093, People’s Republic of China
30
Nankai University, Tianjin 300071, People’s Republic of China
31Peking University, Beijing 100871, People’s Republic of China
32
Seoul National University, Seoul 151-747, Korea
33Shandong University, Jinan 250100, People’s Republic of China
34
Shanghai Jiao Tong University, Shanghai 200240, People’s Republic of China
35Shanxi University, Taiyuan 030006, People’s Republic of China
36
Sichuan University, Chengdu 610064, People’s Republic of China
37Soochow University, Suzhou 215006, People’s Republic of China
38
Sun Yat-Sen University, Guangzhou 510275, People’s Republic of China
39Tsinghua University, Beijing 100084, People’s Republic of China
40a
Istanbul Aydin University, 34295 Sefakoy, Istanbul, Turkey
40bDogus University, 34722 Istanbul, Turkey
40c
Uludag University, 16059 Bursa, Turkey
41University of Chinese Academy of Sciences, Beijing 100049, People’s Republic of China
42
University of Hawaii, Honolulu, Hawaii 96822, USA
43University of Minnesota, Minneapolis, Minnesota 55455, USA
44
University of Rochester, Rochester, New York 14627, USA
45University of Science and Technology of China, Hefei 230026, People’s Republic of China
46
University of South China, Hengyang 421001, People’s Republic of China
47University of the Punjab, Lahore-54590, Pakistan
48a
University of Turin, I-10125, Turin, Italy
48bUniversity of Eastern Piedmont, I-15121, Alessandria, Italy
48c
INFN, I-10125, Turin, Italy
49Uppsala University, Box 516, SE-75120 Uppsala, Sweden
50
Wuhan University, Wuhan 430072, People’s Republic of China
51Zhejiang University, Hangzhou 310027, People’s Republic of China
52
Zhengzhou University, Zhengzhou 450001, People’s Republic of China
Using a data sample collected with the BESIII detector operating at the BEPCII storage ring, we observe
a new neutral state Zcð3900Þ0 with a significance of10.4σ. The mass and width are measured to be
3894.8 2.3 3.2 MeV=c2and29.6 8.2 8.2 MeV, respectively, where the first error is statistical and
the second systematic. The Born cross section foreþe−→ π0π0J=ψ and the fraction of it attributable to
π0Z
cð3900Þ0→ π0π0J=ψ in the range Ec:m:¼ 4.19–4.42 GeV are also determined. We interpret this state
as the neutral partner of the four-quark candidateZcð3900Þ.
DOI:10.1103/PhysRevLett.115.112003 PACS numbers: 14.40.Rt, 13.66.Bc, 14.40.Pq
A new charged charmoniumlike particleZcð3900Þ has recently been observed through its decay to πJ=ψ by BESIII, Belle, and a Northwestern University group using CLEO-c data[1–3]. This state lies just above the threshold for D ¯D production, similar to the bottomoniumlike resonances Zbð10610Þ and Zbð10650Þ that have been observed by Belle at an energy just above theB ¯Bthreshold [4]. BESIII also observed a structure, Zcð3885Þ, in the processeþe− → πðD ¯DÞ∓, with mass close toZcð3900Þ [5]. Because the Zc couples to charmonium and has electric charge, it cannot be a conventional q¯q meson, but must contain at least two light quarks in addition to ac¯c pair. Proposed interpretations for Zc include hadronic molecules, hadroquarkonia, tetraquark states, and kin-ematic effects [6]. The precise structures of the Zc and other“XYZ” states remains unknown, and hence that their further study will lead to a deeper understanding of the strong interaction in the nonperturbative regime.
Progress in clarifying this picture requires measurements of improved precision and searches for additional states. The first definitive observation of a neutralZc state was a BESIII measurement ofZcð4020Þ0→ π0hc[7]. Previously, 3.5σ evidence for a candidate state Zcð3900Þ0decaying to
π0J=ψ was observed in Ref.[3]. In this Letter, we report the
observation ofZcð3900Þ0in the processeþe− → π0π0J=ψ based on data collected with the BESIII detector at the BEPCII electron-positron collider. First measurements of the Born cross section for eþe− → π0π0J=ψ and of the fraction of π0π0J=ψ production attributable to Zcð3900Þ0 as a function of center-of-mass energy (Ec:m:) are also presented. Our data sample has an integrated luminosity of 2809.4 pb−1distributed over theE
c:m:range from 4.190 to
4.420 GeV[8], with an overall measurement uncertainty of 1.0%. The three largest samples have Ec:m: ¼ 4.230 (1091.7), 4.260 (825.7), and 4.360 GeV (539.8 pb−1), with the remainder distributed comparably among seven other energies[9].
BESIII is a general-purpose magnetic spectrometer[10] with a helium-gas-based drift chamber (MDC), a plastic scintillator time-of-flight system (TOF), and a CsI(Tl) electromagnetic calorimeter (EMC) enclosed in a super-conducting solenoidal magnet providing a 1.0 T field. The solenoid is supported by an octagonal flux-return yoke with resistive-plate counters interleaved with steel for muon identification (MUC).
To study the signal response in the BESIII detector, we use a Monte Carlo (MC) package based onGEANT4[11]to
produce simulated samples foreþe− → π0Z0c,Z0c → π0J=ψ andeþe− → π0π0J=ψ without an intermediate Z0c, in both cases with J=ψ → eþe− or μþμ−. We generate eþe− → π0Z0
candZ0c→ π0J=ψ with isotropic angular distributions.
We simulate eþe− → π0π0J=ψ with a generator of final states with aJ=ψ and two pseudoscalars inEVTGEN[12,13]
and no intermediate resonances contributing to the π0 π0 production. To determine theZ0c mass resolution, a signal sample is generated atEc:m:¼ 4.260 GeV with a Z0c mass
of 3.9 GeV=c2 and zero width. In measuring the cross sectionσðeþe− → π0π0J=ψÞ and ratio
R ¼σ(eþe− → π0Zcð3900Þ0→ π0π0J=ψ)
σðeþe− → π0π0J=ψÞ ; ð1Þ
MC samples for eþe−→ π0π0J=ψ, with and without an intermediateZ0c, and using mass and width values obtained in this analysis, are generated at all tenEc:m: points. QED radiative corrections for J=ψ → lþl− are incorporated withPHOTOS [14], and initial-state radiation is simulated
with KKMC[15]using the same parameters as in Ref.[1]. To study background, a generic Yð4260Þ sample and a sample of simulated continuumq¯q production at Ec:m: ¼ 4.260 GeV equivalent to 500 pb−1are used, as in Ref.[1].
Charged tracks are reconstructed from MDC hits. To optimize the momentum measurement, we restrict the angular range of tracks to be j cos θj < 0.93, where θ is the polar angle with respect to the positron beam. We require tracks to pass within 10 cm of the interaction point in the beam direction and within 1 cm in the plane perpendicular to the beam. Electromagnetic showers are reconstructed by clustering EMC energy deposits. Efficiency and energy resolution are improved by including energy deposited in nearby TOF counters. Photons are selected by requiring showers with minimum energies of 25 MeV for j cos θj < 0.8 or 50 MeV for 0.86 < j cos θj < 0.92. The angle between the shower direction and the extrapolation of any track to the EMC must be greater than 5°. A requirement on the EMC timing suppresses electronic noise and deposits unrelated to the event. Candidates for π0→ γγ decays are selected by requiring the diphoton invariant mass to be in the range100 < Mγγ < 160 MeV=c2.
We search foreþe−→ π0π0J=ψ in events with exactly two good oppositely charged tracks and at least four good photons. In reconstructing J=ψ → eþe−, electron candi-dates must satisfyE=p > 0.7, where E is the EMC energy andp is the momentum measured in the MDC. To suppress the small photon and Bhabha background, the two-track opening angle is required to be less than 175° for any eþ (e−) with cosθ > 0.5 (cos θ < −0.5). In selecting
J=ψ → μþμ− we require both muon candidates to satisfy
E=p < 0.3 and at least one to have associated hits in more than six MUC layers.
We reconstruct π0π0J=ψ candidates if the dilepton invariant mass is within the J=ψ signal region (2.95 < Mll< 3.2 GeV=c2). We loop overπ0candidates and select the two that do not share photons and have the smallest χ2¼ χ21Cþ χ24C, where χ21C is the sum of theχ2 values for the two one-constraint (1C) kinematic fits to the π0mass, and χ2
4C is theχ2 for the 4C fit to the π0π0J=ψ
hypothesis requiring 4-momentum conservation. To sup-press the combinatorial background we require that there be fewer than two π0π0 combinations meeting the tighter π0 criterion of120 < Mγγ < 150 MeV=c2.
To search forZ0c and suppress non-π0π0J=ψ events, the event is subjected to a 7C fit, adding mass constraints for both π0s and the J=ψ to 4-momentum conservation. To improve resolutions, for events with χ27C< 230, the 7C-constrained momenta are used to construct Mπ0J=ψ and Mπ0π0. We verified that resonant structures in the π0π0 mass spectrum, such as f
0ð980Þ, do not produce a
peak in theMπ0J=ψdistribution. Figure1shows theπ0J=ψ invariant mass distribution in data and the MC-determined background for Ec:m: ¼ 4.260 GeV. Each π0π0J=ψ event appears twice, once for eachπ0. Background processes are estimated by MC to contribute ∼12% of selected events, dominated byXJ=ψðX ≠ π0π0Þ and multipion final states. Because the location of the lower peak depends on Ec:m: while the higher peak remains fixed, we interpret the excess near 3.9 GeV=c2 as Zcð3900Þ0 production and that near 3.4 GeV=c2 as its kinematic reflection.
We extract the yields and resonance parameters of Zcð3900Þ0 by performing an unbinned maximum
like-lihood fit simultaneously to theπ0J=ψ mass distributions for the three high-statistics samples. The fit lower limit is set to3.65 GeV=c2 to avoid double counting. The signal shape is anS-wave Breit-Wigner with phase-space factor pq, where p is the Z0
c momentum in theeþe− frame and
q is the J=ψ momentum in the Z0
c frame. It is convolved
with a resolution function consisting of three Gaussians with parameters set by fitting the zero-widtheþe−→ π0Z0c MC sample at Ec:m: ¼ 4.260 GeV (average resolution ≈6 MeV=c2). The background shape is an ARGUS
func-tion [16]. We use the same Breit-Wigner and resolution functions for all energy points because resolution depend-ence onEc:m: is determined by MC simulation to be very small. The ARGUS parameters are varied independently in the fit, except that the cutoff is based onEc:m:.
Figure2shows the simultaneous fit to the three π0J=ψ invariant mass distributions, which returns a Zcð3900Þ0 signal with a statistical significance of 10.4σ and a χ2 of 176 for 151 degrees of freedom. Yields at Ec:m:¼ 4.230,
4.260, and 4.360 GeV are225.3 41.0, 83.2 20.5, and 47.5 12.7, respectively, with a sum of 356.0 47.6. The Zcð3900Þ0mass and width values with statistical errors are
3894.8 2.3 MeV=c2 and29.6 8.2 MeV, respectively.
We determine the cross section ratioR and the eþe− → π0π0J=ψ Born cross section as functions of E
c:m: by
measuring yields of Z0c [NðZ0cÞ] and π0π0J=ψ ) 2 (GeV/c ψ J/ 0 π M 4.0 3.5 ) 2 Events/(10 MeV/c 0 5 10 15 20 25 30 35 40
FIG. 1 (color online). Invariant mass distribution for π0J=ψ
candidates in Ec:m:¼ 4.260 GeV data (points). The dashed
histogram shows the MC background and the solid histogram is the sum of this background andπ0π0J=ψ production not from Z0c.
) 2 (GeV/c ψ J/ 0 π M ) 2 Events/(10 MeV/c 100 20 30 40 50 60 70 ) 2 (GeV/c ψ J/ 0 π M -1 (a) 4.230 GeV, 1091.7 pb ) 2 (GeV/c ψ J/ 0 π M ) 2 Events/(10 MeV/c 0 5 10 15 20 25 30 35 40 ) 2 (GeV/c ψ J/ 0 π M -1 (b) 4.260 GeV, 825.7 pb ) 2 (GeV/c ψ J/ 0 π M ) 2 Events/(10 MeV/c 02 3.8 4.0 4.2 4 6 8 10 12 14 16 18 (c) 4.360 GeV, 539.8 pb-1
FIG. 2 (color online). The simultaneously fitted π0J=ψ mass
spectra (55 bins in Mπ0J=ψ) for (a) Ec:m:¼ 4.230,
(b) Ec:m:¼ 4.260, and (c) Ec:m:¼ 4.360 GeV. Dots represent
the data, solid lines represent the fitted results, and dashed lines represent fitted backgrounds.
[Nðπ0π0J=ψÞ]. NðZ0cÞ is determined with a simultaneous fit of the π0J=ψ mass spectra for all ten Ec:m: samples. The signal function is the same as for the fit to the high-statistics samples, with theZcð3900Þ0mass and width fixed to the results of that fit. Background shapes are ARGUS functions with the cutoff based on Ec:m: and other parameters con-strained to be the same for all points.
To obtainNðπ0π0J=ψÞ, the dilepton mass spectra for all energies are fitted simultaneously. The small peaking back-ground from XJ=ψ ðX ≠ π0π0Þ is treated as a systematic error. For this determination the 7C kinematic fit including J=ψ mass constraints is inappropriate and the 4C fit results are used. Events are selected with a cut ofχ24C< 80 based on an optimization considering statistical and systematic uncer-tainties. Each signal shape is a Breit-Wigner convolved with a double Gaussian. The Breit-Wigner is fixed to the width of theJ=ψ and the mass is allowed to vary to allow for possible miscalibration of the momentum scale for reconstructed tracks. The mean of the first Gaussian of the resolution function is fixed to zero, while the other parameters are varied. The background shape is a first-order Chebyshev polynomial with free parameters. In this fit, the parameters of the double-Gaussian and the polynomial are constrained to be the same for all energy points, except for the normali-zation factor.
The fraction of π0π0J=ψ production attributable to Zcð3900Þ0 is determined with Eq. (2), where ϵðZ0cÞ is
the efficiency for extracting the Z0c signal by the fit to the π0J=ψ invariant mass distribution, and ϵ
1ðπ0π0J=ψÞ and
ϵ2ðπ0π0J=ψÞ are efficiencies for determining π0π0J=ψ
yields by fits to dilepton mass distributions for processes without and with an intermediate Z0c, respectively.
R ¼NðZ0cÞ ϵðZ0 cÞ
=
NðZ0 cÞ ϵðZ0 cÞ þ (Nðπ 0π0J=ψÞ −NðZ0cÞ ϵðZ0 cÞϵ2ðπ 0π0J=ψÞ)=ϵ 1ðπ0π0J=ψÞ : ð2ÞThe observed cross section foreþe− → π0π0J=ψ is calcu-lated using Eq. (3), where L is the integrated luminosity andϵðπ0π0J=ψÞ is the weighted average of the efficiencies for events with a Z0c [ϵ2ðπ0π0J=ψÞ] and without a Z0c [ϵ1ðπ0π0J=ψÞ]. The branching ratios BðJ=ψ → eþe−Þ and BðJ=ψ → μþμ−Þ are taken from the PDG[17].
σobs¼ Nðπ0π0J=ψÞ=fL × ϵðπ0π0J=ψÞ
×½BðJ=ψ → eþe−Þ þ BðJ=ψ → μþμ−Þg: ð3Þ
The Born cross section is calculated with
σBorn¼ σobs=½ð1 þ δÞð1 þ δvacÞ, where (1 þ δ) is a
radia-tive correction factor obtained with KKMC [15] and (1 þ δvac) is a vacuum polarization factor following
Ref. [18]. Note that due to the initial state radiation to eþe−resonant structures such asYð4260Þ, (1 þ δ) depends
onEc:m:. The inputs and results are listed in TableI. In cases
where there is no statistically significant signal, the upper limits at 90% confidence level are provided. ForNðZ0cÞ and Nðπ0π0J=ψÞ the errors and upper limits are statistical only.
A cap of 1 is set on theR values. Figures3(a)and3(b)show R and σBorn as functions of Ec:m: with error bars that are
statistical only.
We consider several sources of systematic uncertainty in theZcð3900Þ0mass and width measurements. For the mass determination, the largest uncertainty is that associated with the absolute track momentum scale, estimated to be 2.0 MeV=c2based on the difference between the dilepton
mass determined by the fit and the nominal J=ψ mass. Uncertainty due to the knowledge of the beam energy is estimated to be 1.7 MeV=c2 based on a study of eþe− → μþμ−. Adjusting the cut on χ2
7C by 30 changes
the mass by1.2 MeV=c2, which we assign as the system-atic uncertainty associated with the kinemsystem-atic fit. To assess the uncertainty from the signal parametrization, we change the phase-space factor frompq to p3q3(S wave to P wave) and find a 1.1 MeV=c2 change in the mass. Additional systematic effects associated with fitting-range dependence (0.8), background-shape sensitivity (0.3), andEc:m: depend-ence (0.2 MeV=c2) contribute at a lower level, leading to an overall systematic error in M(Zcð3900Þ0) of 3.2 MeV=c2. The measurement of Γ(Z
cð3900Þ0) has ) ψ J/ 0 π 0 π -e + (eσ ) ψ J/ 0 π 0 π (3900) 0 c Z 0 π -e + (eσ R = 0.0 0.2 0.4 0.6 0.8 1.0 1.2 (a) (GeV) CM E 4.2 4.3 4.4 ) ψ J/ 0 π 0 π → -e + (e Born σ 0 5 10 15 20 25 30 35 40 45 (b) → → →
FIG. 3 (color online). (a) R (see text) and
(b) σBornðeþe−→ π0π0J=ψÞ as functions of Ec:m:. Error bars are statistical only.
a total systematic error of 8.2 MeV, which includes similarly sized contributions from the kinematic fitting procedure (4.6), background shape (4.1), fitting range (3.9), and Ec:m: (3.3 MeV), with a smaller effect due to the signal model (1.7 MeV), and none from the absolute mass scale.
The uncertainties in R and σBorn include contributions from the luminosity (0% for R and 1.0% for σBorn) [9], tracking efficiency (0% and 2.0%) [19], π0 selection efficiency (0% and 4.0%) [20], muon identification effi-ciency (0% and 3.0%), background shape (3.0% and 0.6%), peaking backgrounds (1.4% and 1.4%), fitting range (2.6% and 0.6%), kinematic fit (2.2% and 1.7%), intermediate-state branching ratios (0% and 0.5%), signal parametrization (1.9% and 1.9%), input cross section line shape in KKMC (0% and 0.6%) [21,22], line shape of eþe−→ π0Z0
c(1.1%–12.3% and 0%–3.2%, depending on Ec:m), and
decay models of π0π0J=ψ in the MC (0.2%–6.3% and 0.2%–6.3%). An uncertainty of 0% in R signifies that the effect of that source of systematic uncertainty cancels in the ratio. Results forR and σBornwith systematic errors are given
in TableI. In cases where there is no statistically significant signal, upper limits are defined as sums of 90% confidence level statistical upper limits plus systematic errors.
In summary, we have observed a new charmoniumlike state Zcð3900Þ0 in eþe−→ π0π0J=ψ with a statistical significance of 10.4σ. The mass and width of Zcð3900Þ0 are measured to be 3894.8 2.3 3.2 MeV=c2 and 29.6 8.2 8.2 MeV, respectively. We interpret this state as the neutral partner of the four-quark state candidate Zcð3900Þ, since it decays toπ0J=ψ and its mass is close
to the mass of Zcð3900Þ. The previous report of 3.5σ evidence forZcð3900Þ0[3]included values of the mass and width that are consistent with our results, but are much less precise. We have also measured the cross section ratioR¼ ½σ(eþe−→π0Z
cð3900Þ0→π0π0J=ψ)=σðeþe−→π0π0J=ψÞ
and the Born cross section for eþe−→ π0π0J=ψ in the energy range from 4.190 to 4.420 GeV. The measured Born cross sections are about half of those foreþe−→ πþπ−J=ψ that were measured by Belle[2], consistent with the isospin symmetry expectation for resonances.
The BESIII collaboration thanks the staff of BEPCII and the IHEP computing center for their strong support. This work is supported in part by National Key Basic Research Program of China under Contract No. 2015CB856700; National Natural Science Foundation of China (NSFC)
under Contracts No. 11125525, No. 11235011,
No. 11322544, No. 11335008, and No. 11425524; the Chinese Academy of Sciences (CAS) Large-Scale Scientific Facility Program; the CAS Center for Excellence in Particle Physics (CCEPP); the Collaborative Innovation Center for Particles and Interactions (CICPI); Joint Large-Scale Scientific Facility Funds of the NSFC and CAS under Contracts No. 11179007, No. U1232201, and No. U1332201; CAS under Contracts No. KJCX2-YW-N29, No. KJCX2-YW-N45; 100 Talents Program of CAS; INPAC and Shanghai Key Laboratory for Particle Physics and Cosmology; German Research Foundation DFG under Contract No. Collaborative Research Center CRC-1044; Istituto Nazionale di Fisica Nucleare, Italy; Ministry of Development of Turkey under Contract No. DPT2006K-120470; Russian Foundation for Basic Research under Contract No. 14-07-91152; U.S. Department of Energy
under Contracts No. DE-FG02-04ER41291, No.
DE-FG02-05ER41374, No. DE-FG02-94ER40823, and No. DESC0010118; U.S. National Science Foundation;
University of Groningen (RuG) and the
Helmholtzzentrum fuer Schwerionenforschung GmbH (GSI), Darmstadt; WCU Program of National Research Foundation of Korea under Contract No. R32-2008-000-10155-0.
TABLE I. Efficiencies, yields,R ¼ ½σ(eþe−→ π0Zcð3900Þ0→ π0π0J=ψ)=σðeþe−→ π0π0J=ψÞ, and π0π0J=ψ Born cross sections at each energy point. ForNðZ0cÞ and Nðπ0π0J=ψÞ the errors and upper limits are statistical only. For R and σBorn, the first errors are
statistical and the second errors are systematic. The statistical uncertainties on the efficiencies are negligible. Upper limits of R
(90% confidence level) include systematic errors.
Ec:m: (GeV) (pbL−1) ϵðZ 0 cÞ (%) ϵ1ðπ 0π0J=ψÞ (%) ϵ2ðπ 0π0J=ψÞ (%) ϵðπ 0π0J=ψÞ (%) NðZ 0 cÞ (90% C.L.) Nðπ0π0J=ψÞ R (90% C.L.) 1 þ δ 1 þ δvac σ Born(pb) 4.190 43.1 20.8 20.4 20.1 20.2 <11.1 8.2 3.0 0.71 0.45 0.04 (<1.00) 0.828 1.056 9.0 3.3 0.6 4.210 54.6 21.5 21.0 20.8 20.9 <18.9 26.6 5.4 0.42 0.21 0.03 (<0.72) 0.813 1.057 22.7 4.6 1.5 4.220 54.1 21.6 21.2 20.8 21.1 <12.6 31.9 5.7 0.18 0.14 0.02 (<0.41) 0.810 1.057 27.4 4.9 1.8 4.230 1091.7 22.0 21.1 21.0 21.0 236.8 25.0 825.1 29.8 0.28 0.03 0.02 0.805 1.056 35.4 1.3 2.2 4.245 55.6 22.3 21.6 21.1 21.5 <15.2 49.0 7.1 0.15 0.10 0.02 (<0.32) 0.806 1.056 40.3 5.8 2.7 4.260 825.7 22.6 21.2 21.4 21.2 73.1 16.5 507.3 23.4 0.14 0.03 0.01 0.815 1.054 28.3 1.3 1.8 4.310 44.9 22.5 20.4 20.7 20.5 <7.9 25.5 5.1 0.07 0.12 0.01 (<0.29) 0.916 1.052 24.1 4.9 1.6 4.360 539.8 21.5 18.8 19.1 18.9 41.8 10.8 182.8 14.2 0.20 0.05 0.02 1.038 1.051 13.8 1.1 0.9 4.390 55.2 21.4 17.7 18.4 17.7 <5.2 6.2 2.6 0.00 1.02 0.00 (<0.71) 1.088 1.051 4.7 1.9 0.3 4.420 44.7 21.7 16.8 17.9 16.8 <3.8 2.9 2.1 0.00 0.56 0.00 (<1.00) 1.132 1.053 2.7 1.9 0.2
aAlso at State Key Laboratory of Particle Detection and
Electronics, Beijing 100049, Hefei 230026, People’s
Re-public of China.
b
Also at Ankara University, 06100 Tandogan, Ankara, Turkey.
c
Also at Bogazici University, 34342 Istanbul, Turkey.
dAlso at the Moscow Institute of Physics and Technology,
Moscow 141700, Russia.
eAlso at the Functional Electronics Laboratory, Tomsk State
University, Tomsk, 634050, Russia.
fAlso at the Novosibirsk State University, Novosibirsk,
630090, Russia.
gAlso at the NRC ”Kurchatov Institute, PNPI, 188300,
Gatchina, Russia.
hAlso at University of Texas at Dallas, Richardson, Texas
75083, USA.
iCurrently at Istanbul Arel University, 34295 Istanbul,
Turkey.
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